The government says "progress needs to be made urgently" on Brexit talks with Labour - but that arranging time with the opposition has been "difficult".
Senior figures from both sides have been trying to break the deadlock by agreeing a Brexit deal MPs can support.
No 10 said talks had "been difficult in some areas", including "timetabling".
But Labour leader Jeremy Corbyn said the government "really needs to move on" and change its Brexit agreement to solve the impasse.
He said: "We cannot go on hearing this tired old mantra that the Brexit agreement has to be adhered to."
The deal Theresa May negotiated with the EU has been rejected twice by Parliament, with the withdrawal agreement - the terms on how the UK leaves the bloc, rather than its future relationship with it - defeated a further time.
Weeks of talks resumed between the two parties in Westminster on Tuesday afternoon following the Easter break.
Mrs May's de facto deputy David Lidington was expected to lead for the government.
Shadow Brexit secretary Keir Starmer, shadow chancellor John McDonnell, shadow business secretary Rebecca Long-Bailey and shadow environment secretary Sue Hayman took part on behalf of Labour.
Ahead of the meeting, Sir Keir said "fundamental issues" remained between his party and ministers on a number of key issues.
Some Tory MPs are angry the discussions with Labour are even taking place.
Leading backbencher Nigel Evans called on Mrs May to step down as prime minister "as soon as possible", adding that the PM "had been reaching out to the Labour Party and Jeremy Corbyn, when she should have been reaching out to the people".
Talks between Labour and the government seem to be faltering on two fronts - timing and substance.
Both sides say there has been serious engagement.
But the prime minister wants the talks concluded urgently to give her a chance of cancelling the UK's participation in the European parliamentary elections.
That means getting a deal through Parliament by 22 May.
If it looks like an agreement can't be reached with the opposition quickly, Theresa May wants them jointly to sign up to a series of parliamentary votes that both sides would regard as binding, to try to break the impasse.
But Labour doesn't appear willing to be rushed.
And the main opposition party says Mrs May still needs to erase her red line on a customs union if she is to make progress.
Sources say the issue was discussed at the cabinet today - but, while no votes were taken, there didn't seem to be a majority in favour of doing so.
As things stand, the Brexit deadlock continues - and the European election campaigns are getting under way.
Senior members of the influential 1922 committee of Tory MPs are meeting in Parliament.
Under current party rules, MPs cannot call another no-confidence vote in the prime minister until December - but the committee is expected to discuss whether steps should be taken to try to change that.
The group's joint executive secretary Mr Evans told BBC Radio 4's Today programme the calls for the prime minister to quit had become "a clamour".
"The only way we're going to break this impasse properly is if we have fresh leadership of the Conservative Party," he said.
But prisons minister Rory Stewart said Mrs May was doing a "good job" and deserved "praise not blame".
"It's nothing to do with the individual, it's that people disagree deeply about Brexit," he added.
The comments came after it emerged that Mrs May faces a no-confidence challenge from Tory campaigners.
More than 70 local association chiefs have called for an extraordinary general meeting to discuss her leadership and a non-binding vote is to be held at the National Conservative Convention EGM in May.
If the grass-roots Tory vote showed a lack of confidence - it could put greater pressure on the 1922 Committee to find some way of forcibly removing the PM from office.
That pressure could increase further if the Tories poll badly in local and European elections on 2 and 23 May respectively.
Change UK has launched its European election campaign in Bristol, while Nigel Farage's Brexit Party has unveiled more of its candidates in London.